Question

1. rotation 180° about the origin

Explanation:

Step1: Recall rotation rule

The rule for a 180 - degree rotation about the origin is $(x,y)\to(-x,-y)$.

Step2: Identify vertices

Assume the vertices of the polygon in the original figure are $(x_1,y_1),(x_2,y_2),\cdots$.

Step3: Apply rotation rule

For each vertex $(x_i,y_i)$, the new vertex after 180 - degree rotation about the origin is $(-x_i,-y_i)$. Plot these new vertices to get the rotated figure.

Since we don't have the coordinates of the vertices given in the problem, we can't give the exact new - figure coordinates. But the general method to find the figure after a 180 - degree rotation about the origin is as above.

Answer:

Use the rule $(x,y)\to(-x,-y)$ for each vertex of the original figure to find the vertices of the rotated figure and then plot the rotated figure.